PSI - Issue 39

Lucia Morales-Rivas et al. / Procedia Structural Integrity 39 (2022) 515–527 Author name / Structural Integrity Procedia 00 (2019) 000–000

520

6

is within the short-crack regime. On the other hand, as a lower limit, the FIB defect size was designed to be more critical than other defects such as non-metallic inclusions. By following this strategy, the crack initiation region was not only spatially well defined, but also restricted to the surface of the flat specimen, facilitating the investigation of the crack path. For that purpose, a fatigue strength as an overestimation of the fatigue limit of this material, the former referred to as σ 0_upp throughout this manuscript, was first calculated by making use of Specimen 1 and Specimen 2. For each of these specimens, a load-increase test (LIT) was conducted, each step lasting 10 6 cycles if failure did not occur. Results are summarised in Table 2. The lowest stress amplitude value at which failure occurred, 337.5 MPa, can be considered as an upper limit below which the unknown σ 0 value must lie. The stress range value corresponding to this stress amplitude value, i.e. 675 MPa will be used as σ 0_upp in the following. Table 2. LIT conditions of Specimen 1 and Specimen 2.

Stress amplitude (Sa, MPa)

No. of cycles to failure

No of cycles

Specimen ID

Steps

1 st Step 2 nd Step 3 rd Step 1 st Step 2 nd Step 3 rd Step

293.5 346.8 355.7 205.4

1,000,000 1,000,000

Specimen 1

800,000

1,000,000 1,000,000

Specimen 2

241

337.5

<1,000,000

The FIB design stages shown in the flowchart in Fig. 2 will be discussed in the following. It is worth mentioning that the design of a microstructurally short crack was not feasible in practice, since the microstructural features are in the range of the nano- and submicron-scale. Moreover, as mentioned above, an artificial defect with such a small dimension might not be critical due to other defects like non-metallic inclusions, for instance. In addition, being within the physically short-crack regime, both the crack dimension and the local microstructure are relevant. The version of the Kitagawa-like diagram proposed by Atzori, et al.(2003, Atzori, et al.(2005), which was already described above, was used in order to delimit the range for the FIB defect dimensions. The parameter a 0 was calculated using Eq. 2 considering th = 5.3 MPa.m 1/2 under mode I, a value obtained from the crack growth experiments corresponding to the MECBAIN project Sourmail, et al.(2016). The value σ 0_upp was used instead of the unknown actual σ 0 . Although this approximation would not be conservative from the perspective of mechanical design, for the FIB defect design it implies a more restrictive range for the short-crack regime. The resultant value of a 0 was 18.6 µm. A first estimation of the potential defect dimension was obtained as follows. At this stage, a general solution for the calculation of the maximum stress intensity factor, K I , suggested by Murakami and Endo(1994) (Eq. 5) for surface cracks was taken into consideration. Eq. 5 assumes that the crack dimension is negligible with respect to the specimen geometry and was originally proposed for the tension-compression case ( R =-1). I = 0.65 � √ (5) where refers to the surface of the defect projected in the direction of the maximum principal stress. It has to be noted that Murakami´s solution does not necessarily apply to long cracks for which th is a function of a constant th [Murakami(2012)]. Therefore, in the present work, Eq. 5 was resolved at the border of the short- and long-crack regimes, after considering stress and stress intensity factor ranges. Under these conditions, th can be determined as: ℎ = ℎ 0 . 65� √ (6)